Using the Rain rig, struggling to get IK hand to be constrained to a prop
I figured out what the issue was. It was a dependency loop thing. Earlier in the shot I had the bat constrained to the left hand when she picks the bat off of the floor. And now I added another constraint where the left hand is now constrained to the bat. So having both constraints exist is what was causing what you see in the video above.
Solution was to bake out the animation of the first constraint, delete it, and then add the new constraint. Not ideal, but it worked.